The Yang-Mills α -flow in vector bundles over four manifolds and its applications
Abstract
In this paper, we introduce an α -flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the α -flow with smooth initial value. We prove that the limit of solutions of the α -flow as α 1 is a weak solution to the Yang-Mills flow. By an application of the α -flow, we then follow the idea of Sacks and Uhlenbeck to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek.
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